土木工程专业英语.docx
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土木工程专业英语
土木工程专业英语
4.4ReinforcedConcreteColumn
4.4.1TypesofColumns
Columnsaredefinedasmembersthatcarryloadschieflyincompression.Usuallycolumnscarrybendingmomentaswell,aboutoneorbothaxesofthecross-section,andthebendingactionmayproducetensileforceoverapartofthecross-section.Eveninsuchcases,columnsaregenerallyreferredtoascompressionmembers,becausethecompressionforcesdominatetheirbehavior.Inadditiontothecommontypeofcompressionmembers,i.e.,verticalelementsinstructures,compressionmembersincludearchribs,inclinedrigidframemembers,compressionelementsintrussesorshell.
Columnsmaybeclassifiedbasedonthefollowingdifferentcategories:
(1)Basedonloading,columnsmaybeclassifiedasfollows:
a.Axiallyloadedcolumns,whereloadsareassumedactingatthecentroidofcolumnsection.
b.Eccentricallyloadedcolumns,wheretheloadsareactingatadistanceefromthecentroidofcolumnsection.Thedistanceecouldbealongthexoryaxis,causingmomentseitheraboutthexaxisandyaxis.
c.Biaxiallyloadedcolumns,wheretheloadsareappliedatanypointonthecolumnsection,causingmomentsaboutboththexaxisandyaxissimultaneously.
(2)Basedonlength,columnscanbeclassifiedasfollows:
a.Shortcolumns,wherethecolumn”sfailureisduetothecrushingofconcreteorduetotheyieldingofthesteelbarsunderthefullloadcapacityofthecolumn.
b.Longcolumns(slendercolumns),wherethebucklingeffectandtheslendernessratiomustbetakeintoconsiderationinthedesign,thusreducingtheloadcapacityofthecolumnrelativetothatofashortcolumn.
(3)Basedonlateralreinforcement,columnscanbeclassifiedasfollows(Figure4.24):
a.Columnsreinforcedwithlongitudinalbarsandlateralties.
b.Columnsreinforcedwithlongitudinalbarsandcontinuousspirals.
c.Compositecompressionmembersreinforcedlongitudinallywithstructuralsteelshapes,pipe,ortubing,withorwithoutadditionallongitudinalbars,andvarioustypesoflateralreinforcement.
Themainreinforcementincolumnsislongitudinal,paralleltothedirectionoftheload,andconsistsofbarsarrangedinasquare,rectangular,orcircularpattern.
Lateralreinforcement,intheformofindividualrelativelywidelyspacedtiesoracontinuouscloselyspacedspirals,servesseveralfunctions.Forone,suchreinforcemenisneededtoholdthelongitudinalbarsinpositionsintheformswhiletheconcreteisbeingplaced.Forthispurpose,longitudinalandtransversesteelarewiredtogethertoformcages,whicharethenmovedintotheformsandproperlypositionedbeforeplacingtheconcrete.Foranother,transversereinforcementisneededtopreventthehighlystressed,slenderlongitudinalbarsfrombucklingoutwardbyburstingthethinconcretecover.
Figure4.2
4.4.2ShortColumns
1BehaviororAxiallyLoadedShortColumn
Whenanaxialloadisappliedtoareinforcedconcreteshortcolumn,theconcretecanbeconsideredtobehaveelasticallyuptoalowstressofabout(1/3)f”c.Twodifferenttypesoffailureoccurincolumns,dependingonwhethertiesorspiralsareused.AtiedcolumnfailsattheloadNa(Figure4.25).Atthisload,theconcretefailsbycrushingorshearingoutwardalonginclinedplanes,andthelongitudinalsteelbarsfailbybucklingoutwardbetweenties,asshowninFigure4.26a.Thecolumnfailureoccurssuddenly,muchlikethefailureofaconcretecylinder.
Inaspirallyreinforcedcolumn,whenthesameloadNaisreached,thelongitudinalsteelandtheconcretewithinthecorearepreventedfrommovingoutwardbythespiral.Theconcreteintheoutershell,however,notbeingsoconfined,doesfail;i.e.,theoutershellspallsoffwhenNaisreached,asshowninFigure4.26b.Itisatthisstagethattheconfiningactionofthespiralhasasignificanteffect,andifsizablespiralsteelisprovided,theloadwillultimatelyfailthecolumnbycausingthespiralsteeltoyield.Theaxialstrainwhenthecolumnfailscanbemuchlargerthanthatatwhichtheshellspallsoff.
Figure4.25Load-deformationoftiedandspirallyreinforcedconcretecolumn
Figure4.26Failureoftiedandspirallyreinforcedconcretecolumn
Iftheloadonthecolumnisincreasedtoreachitsultimatestrength,theconcretewillreachthemaximumstrengthandsteelwillreachitsyieldstrength,fy.SeeFigure4.27.theultimatebearingcapacityofashortcolumnreinforcedwithlongitudinalbarsandlateraltiescanbewrittenasfollows
Nu=f`yA`s+fcAc(4.4.1)
Where,
A`s=reinforcementarea
f`y=reinforcementyieldstrength
Ac=concretesectionarea
fc=concreteprismaticcompressivestrength
2.ShortColumnsunderCombinedAxialForceandMoment
WhenamemberissubjectedtocombinedaxialcompressionNandmomentM,suchasinFigure4.28a,itisusuallyconvenienttoreplacetheaxialloadandmomentwithanequalloadNappliedateccentricitye=M/N,asinFigure4.28b.Thetwoloadingsarestaticallyequivalent.Allcolumnsmaythenbeclassifiedintermsoftheequivalenteccentricity.
Figure4.27Stressandforceatultimatestrengthofaxialloadedcolumn
Figure4.28Equivalenteccentricityofcolumnload
(1)Failremodesofcolumns
Underthecombinedactionsofaxialforceandmoment,therearetwotypesoffailuremodesofcolumn(a)balancedfailure,(b)compressionfailure,whentheneutralaxisisoutsidethesection,causingcompressionthroughoutthesection,and(c)tensionfailure,whentheneutralaxisiswithinthesection,developingtensilestrainontheleftoftheneutralaxis.
Balancedfailure
Underthismodeoffailure,yieldingofthetensilesteelonthefarsideofthecolumnoccurssimultaneouslywiththeattainmentoflimitcompressivestrainof0.0033inconcrete.
Compressionfailure
Compressionfailureofthecolumnoccurswhen(a)therelativeeccentricityeo/hoissmall,or(b)althoughtherelativeeccentricityeo/holarge,thetensionreinforcementratioislarge.Columnshavingsmallrelativeeccentricityaregenerallycharacterizedbycompressionovertheentireconcretesection,butcolumnswithlargeeccentricityaresubjectedtotensionovertensionoveratleastapartofthesection.Columnsofthistypefailbycrushingoftheconcreteandcompressiveyieldingofthesteelonthesideneartheload,whilethereinforcementonthesidefarthestfromtheloaddoesnotyield.SeeFigure4.29b.
Figure4.29Failuremodesofcolumns
Tensionfailure
Tensionfailureoccurswhen(a)therelativeeccentricitye0/h0islarge,and(b)thetensionreinforcementratioismoderate.Thelongitudinalsteelonthesidefarthestfromtheloadyieldsfirst.Gradually,withtheincreaseoftensilestrain,thecompressivestrainreaches0.0033atthecompressiveedgeandcompressionreinforcementyields.
(2)Capacityofshortcolumnsundercombinedaxialforceandmoment
Underthecombinedactionsofaxialforceandmoment,astrengthinteractiondiagram(seeFigure4.30)generallydescribesthecapacityenvelopeofacolumn.Thestrengthinteractiondiagramdefinesthefailureloadandfailuremomentforagivencolumnforthefullrangesofeccentricityfromzerotoinfinity.Foranyeccentricity,thereisauniquepairofvalueof(Mu,Nu)thatwillproducetheincipientfailure.ThatpairsofvaluescanbeplottedasapointonagraphrelatingNuandMu.Anyradicallinerepresentsaparticulareccentricityeo=M/N.Loaddemandpoints(M,N)fromallloadcombinationsmustfallinsidethe(M0,N0)capacityenvelope;otherwise,thecolumnisconsideredinadequateandshouldberedesigned.
Figure4.30Strengthinteractiondiagram
Theupperpointofaninteractioncurveisthecaseofpureaxialcompression.Wheretheinteractioncurveintersectswiththemomentaxis,thecolumnisunderpurebending,inwhichcasethecolumnbehaves^likeabeam.Thepointofmaximummomentontheinteractiondiagramcoincideswiththebalancedcondition.Theextremeconcretefiberstrainreachesultimatestrain(0.0033)simultaneouslywithyieldingoftheextremelayerofsteelontheoppositeside(fy/Es=0.002).
TheinteractiondiagramfurtherrevealsthatastheaxialforceNubecomeslargerthesectioncancarrysmallerMubeforefailinginthecompressionzone.Thereverseisthecaseinthetensionzone,wherethemomentcarryingcapacityMuincreaseswiththeincreaseofaxialloadN„.Inthecompressionfailurezone,thefailureoccursduetooverstrainingofconcrete.Thelargeaxialforceproduceshighcompressivestrainofconcretekeepingsmallermarginavailableforadditionalcompressivestrainduetobending.Ontheotherhand,inthetensionfailurezone,yieldingofsteelinitiatesfailure.Thistensilesteelstressreduceswiththeadditionalcompressivestressduetoadditionalaxialload.Asaresult,furthermomentcanbeapplieduntilthecombinedstressofsteelduetoaxialforceandincreasedmomentreachestheyieldstrength.
Figure4.31showsamemberloadedparalleltoitsaxisbyacompressiveforceNataneccentricitye0measuredfromthecenterline.TheactualgeometricalshapeoftheconcretestressesdistributionisshowninFigure4.31a.Justasforsimplebending,theactualconcretecompressivestressdistributionisreplacedbyanequivalentrectangulardistributionhavingdepth.r.Equilibriumbetweenexternalandinternalaxialforcesrequiresthat
Figure4.31Actualandequivalentrectangularstressdistributionofeccentricallyloadedcolumnatultimatestrength
Inaddition,sumofthemomentsoftheconcretecompressivestress,reinforcementforceandtheexternalforceNaboutthecenterlineoftheresultantforceinthetensionreinforcementmustequaltozero
where.
e